National Instruments NI MATRIXx Xmath - Manual (Page 34)

Chapter 2 Additive Error Reduction
© National Instruments Corporation 2-11 Xmath Model Reduction Module
Related Functions
balance() , truncate() , redschur() , mreduce()
truncate( )
SysR = truncate(Sys,nsr,{VD,VA})
The truncate( ) function reduces a system Sys by retaining the first
nsr states and throwing away the rest to form a system SysR .
If for Sys one has,
the reduced order system (in both continuous-time and discrete-time cases)
is defined by A
11
, B
1
, C
1
, and D. If Sys is balanced, then SysR is an
approximation of Sys achieving a certain error bound. truncate( ) may
well be used after an initial application of balmoore( ) to further reduce
a system should a larger approximation error be tolerable. Alternatively, it
may be used after an initial application of
balance( ) or redschur( ) .
If Sys was calculated from redschur( ) and VA,VD were posed as
arguments, then SysR is calculated as in redschur( ) (refer to the
redschur( ) section).
truncate( ) should be contrasted with mreduce( ) , which achieves a
reduction through a singular perturbation calculation. If Sys is balanced,
the same error bound formulas apply (though not necessarily the same
errors),
truncate( ) always ensures exact matching at s =
∞ (in the
continuous-time case), or exacting matching of the first impulse response
coefficient D (in the discrete-time case), while
mreduce( ) ensures
matching of DC gains for Sys and SysR in both the continuous-time and
discrete-time case. For a additional information about the truncate( )
function, refer to the Xmath Help.
Related Functions
balance() , balmoore() , redschur() , mreduce()
A
A
11
A
12
A
21
A
22
= B
B
1
B
2
= C C
1
C
2
=